| 偏微分方程边值反问题的数值方法研究 |
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| 引用本文： | 易苗,刘扬.偏微分方程边值反问题的数值方法研究[J].数学杂志,2017,37(5):1040-1046. |
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| 作者姓名： | 易苗 刘扬 |
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| 作者单位： | 武汉大学数学与统计学院, 湖北武汉 430072,武汉理工大学理学院, 湖北武汉 430070 |
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| 基金项目： | 国家自然科学基金（11201358）；中央高校基本科研业务费专项资金资助（2015IA007）. |
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| 摘 要： | 本文研究了奇异积分方程在反边值问题中的应用问题.利用圆周上的自然积分方程及其反演公式,把Laplace方程的边值反问题转化为一对超奇异积分方程和弱奇异积分方程的组合,通过选取三角插值近似奇异积分的计算并构造相应的配置格式,并使用Tikhonov正则化方法求解所得到的线性方程组.数值实验表明了该方法的有效性.
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| 关 键 词： | 边值反问题 奇异积分方程 三角插值 Tikhonov正则化 |
| 收稿时间： | 2016/1/9 0:00:00 |
| 修稿时间： | 2016/4/15 0:00:00 |
NUMERICAL METHODS FOR SOLVING INVERSE BOUNDARY VALUE PROBLEM OF PARTIAL DIFFERENTIAL EQUATION |
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| YI Miao and LIU Yang.NUMERICAL METHODS FOR SOLVING INVERSE BOUNDARY VALUE PROBLEM OF PARTIAL DIFFERENTIAL EQUATION[J].Journal of Mathematics,2017,37(5):1040-1046. |
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| Authors: | YI Miao and LIU Yang |
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| Institution: | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China and School of Science, Wuhan University of Technology, Wuhan 430070, China |
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| Abstract: | In this paper, we study the application problem of singular integral equation in the inverse boundary value problem. Using the natural integral equation and its inversion formula on a circle, we transformed the Laplace equation inverse boundary value problem into a combination of a hypersingular integral equation and a weakly singular integral equation, then construct the corresponding collocation scheme based on the trigonometric interpolation, and use the Tikhonov regularization to solve the resulting linear equations. Numerical experiments show the effectiveness of the method. |
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| Keywords: | inverse boundary value problem singular integral equation trigonometric interpolation Tikhonov regularization |
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